Question

question 6 of 10
fill in the blank. in the triangle below, ( z^circ = ) ____ ( ^circ ).
right triangle with right angle, one angle 52°, side adjacent to 52° is 35, hypotenuse y, base x, angle at left vertex z°
answer here
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Explanation:

Step1: Recall triangle angle sum property

In a right - triangle, one angle is \(90^{\circ}\), and the sum of the interior angles of a triangle is \(180^{\circ}\). Let the right angle be \(90^{\circ}\), one acute angle be \(52^{\circ}\), and the other acute angle be \(z^{\circ}\). So we have the equation \(z + 52+90=180\).

Step2: Solve for z

First, simplify the left - hand side of the equation: \(z + 142 = 180\). Then, subtract 142 from both sides of the equation: \(z=180 - 142\). Calculating the right - hand side, we get \(z = 38\).

Answer:

\(38\)